| Since the publication of Shannon's theory of one terminal source coding, a number of interesting extensions have been derived by researchers such as Slepian-Wolf, Wyner, Ahlswede-Körner, Wyner-Ziv, Berger et al. and Berger-Yeung. Specifically, the achievable rate or rate-distortion region has been described by a first order information-theoretic functional of the source statistics in each of the above cases. At the same time various source coding problems have also remained unsolved: Notable two terminal examples include the joint distortion problem, where both sources are reconstructed under a combined distortion criterion, as well as the partial side information problem, where one source is reconstructed under a distortion criterion using information about the other (side information) available at a certain rate (partially). In this thesis, we describe the rate-distortion region for each of these open problems by an infinite order information-theoretic functional of source distribution. However, our description does not immediately give a plot of or even an algorithm to plot the corresponding achievable region.;In fact, we set distributed source coding problems in a general framework and take a unified structural view of not only the above open problems but any two-terminal problem with noncooperative encoding. The distortion criteria, if applicable, are required to apply to single letters and be bounded. The key to the above unification is held by a fundamental source coding principle which dissociates the underlying source coding mechanism from the applicable distortion criteria and extends the typicality arguments of Shannon and Wyner-Ziv. We generalize our theory further to show that distortion criteria can also be dissociated from the underlying coding mechanism in an arbitrary multiterminal setup. As in the two-terminal problem, the general achievable region permits an infinite order information-theoretic description. Moreover, we validate our analysis by rederiving known coding theorems using our technique: Our infinite order descriptions are shown to simplify to the expected first order in the known cases. |
